Math Problem Statement

List the numbers in order from least to greatest: √5, 3.7, 1/2, -4.

Solution

The task asks to list the numbers in order from least to greatest. The given numbers are:

5,3.7,12,4\sqrt{5}, 3.7, \frac{1}{2}, -4

Step 1: Approximate the values

  1. 52.236\sqrt{5} \approx 2.236
  2. 3.73.7 (already in decimal form)
  3. 12=0.5\frac{1}{2} = 0.5
  4. 4-4 (already in integer form)

Step 2: Arrange the numbers

Now, let's compare these values:

  • 4-4
  • 0.50.5
  • 2.2362.236
  • 3.73.7

Final Order:

From least to greatest, the numbers are: 4,12,5,3.7-4, \frac{1}{2}, \sqrt{5}, 3.7

Would you like further details or have any questions?

Here are 5 related questions:

  1. How would you calculate the square root of a non-perfect square like 5?
  2. Can you explain how to convert fractions to decimals?
  3. How do you compare negative numbers with positive ones?
  4. What is the significance of approximating irrational numbers like 5\sqrt{5}?
  5. How does the order of operations affect how we handle expressions with radicals?

Tip: Always approximate square roots of non-perfect squares to compare them easily with other numbers.

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Math Problem Analysis

Mathematical Concepts

Ordering Real Numbers
Square Roots
Decimal and Fraction Conversion

Formulas

√x (Square Root)
Fraction to Decimal Conversion

Theorems

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Suitable Grade Level

Grades 6-8